Getal & Ruimte (12e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.4 Logaritmen |
opgave 1Bereken. 1p a \({}^{9}\!\log(81)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{9}\!\log(81) = {}^{9}\!\log(9^{2}) = 2\) 1p 1p b \({}^{4}\!\log(4)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{4}\!\log(4) = {}^{4}\!\log(4^{1}) = 1\) 1p 1p c \(\log(1\,000\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(1\,000\,000) = \log(10^{6}) = 6\) 1p 1p d \({}^{3}\!\log(\frac{1}{27})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{3}\!\log(\frac{1}{27}) = {}^{3}\!\log(3^{-3}) = -3\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{4}}\!\log(\frac{1}{16})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{4}}\!\log(\frac{1}{16}) = {}^{\frac{1}{4}}\!\log(\frac{1}{4}^{2}) = 2\) 1p 1p b \({}^{\frac{1}{6}}\!\log(36)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{6}}\!\log({}^{\frac{1}{6}}\!\log(36)) = {}^{\frac{1}{6}}\!\log(\frac{1}{6}^{-2}) = -2\) 1p 1p c \({}^{4}\!\log(4 \sqrt{4})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{4}\!\log(4 \sqrt{4}) = {}^{4}\!\log(4^{1} ⋅ 4^{\frac{1}{2}}) = {}^{4}\!\log(4^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p d \({}^{3}\!\log(3^{2{,}4})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{3}\!\log(3^{2{,}4}) = 2{,}4\) 1p |